Quentin F. Stout
University of Michigan
Abstract: Let B(l_{p},l_{q}) denote the bounded linear operators from l_{p} to l_{q}, for 1 ≤ p, q ≤ ∞. Termwise multiplication of two bounded linear operators in B(l_{p},l_{q}) yields another bounded linear operator in B(l_{p},l_{q}), called their Schur product (and sometimes misnamed their Hadamard product). The Schur product thus defines a commutative Banach algebra structure on B(l_{p},l_{q}), even though when p ≠ q there was no natural product on this space, and when p = q there is a natural product but it is not commutative.
The maximal ideal spaces of these algebras are shown to be points in the Stone-Čech compactification of N x N, where N denotes the natural numbers. Various ideals and their hulls are examined, and several open questions are posed.
Keywords: Schur multiplication, Banach algebra, maximal ideal space, Stone-Cech compactification, operator theory, l_{p} spaces, spectral synthesis
Complete paper. This paper appears in Journal of Operator Theory 5 (1981), pp. 231-243.
Here is some related work in operator theory.
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